Symmetric graph properties have independent edges

Symmetric Graph Properties Have Independent Edges

In the study of random structures we often face a trade-off between realism and tractability, the latter typically enabled by independence assumptions. In this work we initiate an effort to bridge this gap by developing tools that allow us to work with independence without assuming it. Let Gn be the set of all graphs on n vertices and let S be an arbitrary subset of Gn, e.g., the set of all gra...

Product Measure Approximation of Symmetric Graph Properties

Random structures often present a trade-off between realism and tractability, the latter predominantly enabled by independence. In pioneering random graph theory, Erdős and Rényi originally studied the set of all graphs with a given number of edges, seeking to identify its typical properties under the uniform measure, i.e., the G(n,m) model of random graphs. However, this approach quickly prese...

The Maximum Number of Edges in a Strongly Multiplicative Graph

Hidden Edges in Graph Coloring

A theory about the implication structure in graph coloring is presented. Discovering hidden relations is one of the most relevant activities in every scientific discipline. The development of mathematical models to study and discover such hidden relations is of the most highest interest. The main contribution presented in this work is a model of hidden relations materialized as implicit edges i...

the maximum number of edges in a strongly multiplicative graph

0